Role of Average Energy and Plane Waves in the Schrodinger Equation

n an earlier note (1), it was argued the time-independent Schrodinger equation may be written in a momentum form by using W(x)=Sum over p  fp exp(ipx)= wavefunction and V(x)=Sum over p Vp exp(ipx). This lead to an equation for each plane wave of the form:

 p*p/2m fp + Sum over j+k=p  Vj fk = E fp ((1)). In this note, we try to argue that ((1)) does not need to follow from the time-independent Schrodinger equation, but rather seems to be a consequence of fp, which is related to conditional probability P(p/x).